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Equilateral Sets in l n p

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Abstract

We show that for every odd integer p ≥1 there is an absolute positive constantc p , so that the maximum cardinality of a set of vectors in R n such that the l p distance between any pair is precisely 1, is at most c p n log n. We prove some upper bounds for other l p norms as well.

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Authors and Affiliations

  1. Institute for Advanced Study, Princeton University, 08540, Princeton, NJ, USA

    Noga Alon

  2. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    Noga Alon

  3. Mathematical Institute, Academy of Sciences of the Czech Republic, Prague, Czech Republic

    Pavel Pudlák

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  1. Noga Alon
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  2. Pavel Pudlák
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Correspondence to Noga Alon.

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Alon, N., Pudlák, P. Equilateral Sets in l n p . Geom. funct. anal. 13, 467–482 (2003). https://doi.org/10.1007/s00039-003-0418-7

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  • DOI: https://doi.org/10.1007/s00039-003-0418-7

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